1. Field of the Invention
The present invention generally relates to a method and apparatus for sensor replication, and more particularly to a method and apparatus for sensor replication for ensemble averaging in micro-electromechanical systems (MEMS).
2. Description of the Related Art
A MEMS-based servo positioning device, when enclosed within a disturbance free housing, is capable of producing high precision mechanical displacement. Noise inherent in a position sensor that is embedded in a MEMS-based servo control system determines the precision of the integrated system.
To improve the precision, noise generated in a position sensor [1-sigma (σ)] must be reduced. However, there is a fundamental limit to minimizing the sensor noise, and creative methods are required to circumvent the performance limitation.
More generally, a sensing process requires a transducer and a signal conditioning method. A transduction process not only generates a useful signal, but inevitably produces a noise component, thus reducing the accuracy of the sensing process. Using instrumentation-quality electronics, the total noise from a sensor can be kept to a minimum, but the noise due to the transduction process cannot be eliminated completely. Position sensing of an object can be derived from a multitude of transduction processes. Among non-contact transduction processes where frictionless movement is desired, optical, thermal and/or magnetic coupling effects can be employed.
FIG. 1 shows some exemplary elements of a single-axis position servo control system 100 including a MEMs positioning system 140. A position sensor 1404 of the system 140 illustrated in this example is sensitive to a location of an edge 1405 of a movable device 1403 designed to move with respect to a stationary frame 1402.
The sensor voltage V(t) includes a noise component n(t). A servo controller 125 produces a control signal U from the indicated position error signal (e.g., provided from an adder or summer unit (e.g., summing junction) 120, and drives a power signal (e.g., typically an electric current), via a driver 130, into an actuator 1401.
It is noted that an absolute position is provided from the MEMs-based position sensor 1404 back to an adder 115, which also receives sensor noise n(t), thereby to output a measured or indicated position V(t). The measured or indicated position V(t) combined with a target position signal, results in the measured or indicated position error signal output by the adder 120 to the servo controller 125, as described above.
The servo controller 125 and associated electronics (e.g., for measuring the position, generating control signal U, etc.) are a subset of a system controller 110. The system controller has a memory 150 (e.g., a memory bank) in which servo system parameters are stored during the power-on operation of the servo control system 125.
FIG. 2 elaborates the parameters of a position sensor employed to establish the advantages and merit of the present invention. As shown in FIG. 2, a single sensor noise model 200 is shown receiving an input from a MEMs-based mechanical position sensor 225 based on the mechanical motion 215 of a MEMs device. A noiseless (ideal) sensor output 2002 is shown being input to an adder 2003, which also receives a 10 MHz wide band noise (1-sigma=10*12.5 nm).
The adder 2003 provides an output to a lowpass filter 230 (e.g., having a cutoff of 100 kHz), which in turn provides an analog output 240 of a single MEMs position sensor 240 to a sampler 250. The sampler 250 provides an output to a low pass filter (LPF) 260 which is a second order digital filter.
The LPF 260 provides a measured or indicated position (filtered) V(t) to a servo controller 205. The servo controller outputs a signal to an amplifier 210 to control the mechanical motion of the MEMs device.
It is noted that exemplarily the transducer is based on a thermal coupling effect which is not the subject of the present invention. The sensor dynamics 2001 are dominated by the thermal coupling effect which has a time constant of 50 μs, and is characterized by a first order system.
The noise power spectrum measured after the 100 kHz second order analog low-pass filter 230 contained a noise equivalent to 12.5 nm (1-sigma). The targeted displacement range of the position sensor is 100 μm. In order to demonstrate the invention through simulation and as mentioned above, the sensor noise at the source is represented by a wide-band (10 MHz) noise (10*12.5 nm 1-sigma).
In order to capture the effect of sensor noise in this application under realistic operating conditions, a servo control system is required. An industry-proven proportional-integral-derivative (PID) positioning servo system (e.g., servo controller 205) is employed for the MEMS-based positioning device. A characteristic PID controller transfer function, for example, in analog form, is represented by the following expression:Controller(Output/Input)=(kP+kDs+kI/s)
where gains kP, kD, and kI are proportional, derivative and integral gains, and ‘s’ is the Laplace transform operator. The parameterization process to compute the gains is well-known in the field. A control system designer would use a dynamic model of the scanner and would derive the gain values to achieve an optimum servo controller design.
It is noted that if a MEMs-based sensor has too much noise, one could use a low pass filter (as described above), but such a low pass filter introduces a phase lag.
FIGS. 3A-3B show the open loop transfer function of a characteristic MEMS-based position control system with a digital-PID controller. A crossover frequency of 650 Hz is used in this study, as shown in FIG. 3A. The controller is cascaded with a digital low pass filter (LPF) with a 4 kHz crossover frequency. FIG. 3B shows that the phase loss in this region degrades the settling performance.
FIG. 4 shows the position sensor output obtained after the 4 kHz LPF and estimated (through simulation) position of the MEMS device. It is noted that the stand alone (i.e., without any servo action) sensor noise component has 1-sigma of 12.5 nm.
However, after 4 kHz LPF and under closed loop servo conditions, the sensor output is reduced to 1-sigma of 4.6 nm (e.g., this component is referred to as indicated or measured sensor output) because the MEMS system actually follows the sensor noise (an undesirable but necessary effect of the servo) at lower than crossover frequencies.
The low frequency noise following capability of a servo actually produces physical motion (e.g., referred to as absolute position) and the corresponding motion is detrimental to the precision centric performance of a system. The estimated value of the absolute position is 3.6 nm even though the noisy sensor output indicates 4.6 nm. It is noted that, if an ideal sensor (i.e., zero noise component) was employed to monitor the motion of the mechanical device, then it would measure 3.6 nm.
The position accuracy of the servo control system can be improved by reducing the corner frequency “fc” of the low-pass filter shown in FIG. 2. However, reducing the LPF corner frequency introduces additional phase lag and penalizes the dynamic performance, such as settling time, unfavorably.
Thus, prior to the present invention, there has been no method or system which shows how this limitation can be circumvented.